This is of course a result of both the utter failure of these mathematical models to predict the crisis and the role of some of these models in actually causing the crisis.

Columnist Anatole Kaletsky recently published an article where he criticized these models. I don't agree with all of his arguments of formulations, but I certainly agree with his conclusion of the failure of mathematical models.

This article has evoked response from several people, including Paul Krugman, who apparently completely failed to grasp the point of the article, as the claim that Keynes didn't use mathematical was met with a supposed example that Keynes did do mathematical modeling. Krugman apparently didn't notice that the point of the was that this wasn't a good thing.

Krugman however does concede that Keynes' model wasn't particularly advanced in its mathematics. Here is the example that Krugman quotes:"Let Z be the aggregate supply price of the output from employing N men, the relationship between Z and N being written Z = φ(N), which can be called the aggregate supply function. Similarly, let D be the proceeds which entrepreneurs expect to receive from the employment of N men, the relationship between D and N being written D = f(N), which can be called the aggregate demand function.

Now if for a given value of N the expected proceeds are greater than the aggregate supply price, i.e. if D is greater than Z, there will be an incentive to entrepreneurs to increase employment beyond N and, if necessary, to raise costs by competing with one another for the factors of production, up to the value of N for which Z has become equal to D. Thus the volume of employment is given by the point of intersection between the aggregate demand function and the aggregate supply function; for it is at this point that the entrepreneurs’ expectation of profits will be maximised. The value of D at the point of the aggregate demand function, where it is intersected by the aggregate supply function, will be called the effective demand. Since this is the substance of the General Theory of Employment, which it will be our object to expound, the succeeding chapters will be largely occupied with examining the various factors upon which these two functions depend."

What Keynes is actually saying here in an unnecessarily complicated way is simply that employers will hire workers as long as they think that hiring them will bring in more extra revenues than extra costs. Something which illustrates what I've long said is the best case scenario for mathematical models, namely that it will say the same thing as you could say with verbal logic, something which of course violate the principle of Occam's razor.

Yet the best "defense" it comes up with is that non-mathematical theories (which are called "intuition") can be false too, and that this supposedly doesn't prove that mathematical models aren't illegitimate.

But while it is certainly true that what he calls "intuitive" reasoning often produces false theories, the point is that mathematical modeling can never give a more accurate description than verbal reasoning. At best, as in the quote from Keynes above, it simply expresses in an unnecessarily complicated way what can be derived from verbal logic. In many cases, though, the translation into mathematics makes correct theories false. One example of this is the focus on equilibrium (a focus necessitated by the fact that the first order condition of a Lagrange multiplier is that the partial derivative is zero, which in this context translated into English means that no further economic gains can be made, or in other words that equilibrium is reached), which in turn means that there are no room for one of the key elements of economic reality, namely entrepreneurship.

The description of verbal theory as "intuition" is also misleading. "Intuition" is usually defined as acquiring knowledge without the use of reason or inference, yet verbal (praxeological) logic is just as based on reason as mathematics. Verbal logic can also be made formal if you want to, in the form of a syllogism as I did here.

2 Comments:

Taleb in his book "Fooled by Randomness" also mentions Anatole Kaletksy on [p.62]: "There are hordes of thoughtful [financial] journalists in the business ...Anatole Kaletsky...Jim Grant...Alan Abelson"

This is a very interesting post and exactly my feelings from studying Economics and Econometrics. The discussion kind of reminds me of 'geometric logic': http://www.youtube.com/watch?v=3zgeQmzV9kk :)/Daniel

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